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Congruence property in orbifold theory

Authors: Chongying Dong and Li Ren
Journal: Proc. Amer. Math. Soc. 146 (2018), 497-506
MSC (2010): Primary 17B69
Published electronically: August 31, 2017
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Abstract: Let $ V$ be a rational, selfdual, $ C_2$-cofinite vertex operator algebra of CFT type, and $ G$ a finite automorphism group of $ V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated to $ V$ and $ G$ is a congruence subgroup. In particular, the $ q$-character of each irreducible twisted module is a modular function on the same congruence subgroup. In the case $ V$ is the Frenkel-Lepowsky-Meurman's moonshine vertex operator algebra and $ G$ is the monster simple group, the generalized McKay-Thompson series associated to any commuting pair in the monster group is a modular function.

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Additional Information

Chongying Dong
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064

Li Ren
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China

Received by editor(s): October 17, 2016
Received by editor(s) in revised form: March 27, 2017
Published electronically: August 31, 2017
Additional Notes: The first author was supported by a NSF grant DMS-1404741 and China NSF grant 11371261
The second author was supported by China NSF grant 11301356
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2017 American Mathematical Society

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